Properties

Label 3150.2.bf.e.1151.8
Level 3150
Weight 2
Character 3150.1151
Analytic conductor 25.153
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.bf (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1151.8
Character \(\chi\) = 3150.1151
Dual form 3150.2.bf.e.1601.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.43194 - 1.04195i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.43194 - 1.04195i) q^{7} -1.00000i q^{8} +(1.38605 + 0.800236i) q^{11} +0.770726i q^{13} +(1.58515 - 2.11833i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.76107 - 3.05027i) q^{17} +(3.06818 - 1.77141i) q^{19} +1.60047 q^{22} +(-2.79527 + 1.61385i) q^{23} +(0.385363 + 0.667468i) q^{26} +(0.313613 - 2.62710i) q^{28} -0.700774i q^{29} +(1.13725 + 0.656589i) q^{31} +(-0.866025 - 0.500000i) q^{32} -3.52215i q^{34} +(0.457320 + 0.792101i) q^{37} +(1.77141 - 3.06818i) q^{38} +4.88167 q^{41} +9.26963 q^{43} +(1.38605 - 0.800236i) q^{44} +(-1.61385 + 2.79527i) q^{46} +(-1.33635 - 2.31462i) q^{47} +(4.82867 - 5.06793i) q^{49} +(0.667468 + 0.385363i) q^{52} +(-8.04572 - 4.64520i) q^{53} +(-1.04195 - 2.43194i) q^{56} +(-0.350387 - 0.606888i) q^{58} +(1.56198 - 2.70542i) q^{59} +(-9.43214 + 5.44565i) q^{61} +1.31318 q^{62} -1.00000 q^{64} +(3.40818 - 5.90314i) q^{67} +(-1.76107 - 3.05027i) q^{68} +6.47930i q^{71} +(9.55835 + 5.51852i) q^{73} +(0.792101 + 0.457320i) q^{74} -3.54282i q^{76} +(4.20460 + 0.501930i) q^{77} +(-1.45086 - 2.51296i) q^{79} +(4.22765 - 2.44083i) q^{82} -11.9777 q^{83} +(8.02773 - 4.63481i) q^{86} +(0.800236 - 1.38605i) q^{88} +(4.40369 + 7.62742i) q^{89} +(0.803059 + 1.87436i) q^{91} +3.22770i q^{92} +(-2.31462 - 1.33635i) q^{94} -5.31224i q^{97} +(1.64779 - 6.80329i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 12q^{4} + 4q^{7} + O(q^{10}) \) \( 24q + 12q^{4} + 4q^{7} - 12q^{16} + 12q^{19} - 4q^{28} - 28q^{37} - 96q^{43} - 8q^{46} - 52q^{49} + 12q^{52} - 8q^{58} - 12q^{61} - 24q^{64} + 4q^{67} + 12q^{73} + 4q^{79} + 68q^{91} - 24q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) 2.43194 1.04195i 0.919187 0.393821i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0 0
\(11\) 1.38605 + 0.800236i 0.417910 + 0.241280i 0.694183 0.719799i \(-0.255766\pi\)
−0.276273 + 0.961079i \(0.589099\pi\)
\(12\) 0 0
\(13\) 0.770726i 0.213761i 0.994272 + 0.106880i \(0.0340862\pi\)
−0.994272 + 0.106880i \(0.965914\pi\)
\(14\) 1.58515 2.11833i 0.423648 0.566147i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.76107 3.05027i 0.427123 0.739799i −0.569493 0.821996i \(-0.692860\pi\)
0.996616 + 0.0821974i \(0.0261938\pi\)
\(18\) 0 0
\(19\) 3.06818 1.77141i 0.703888 0.406390i −0.104906 0.994482i \(-0.533454\pi\)
0.808794 + 0.588092i \(0.200121\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 1.60047 0.341222
\(23\) −2.79527 + 1.61385i −0.582854 + 0.336511i −0.762267 0.647263i \(-0.775914\pi\)
0.179413 + 0.983774i \(0.442580\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0.385363 + 0.667468i 0.0755759 + 0.130901i
\(27\) 0 0
\(28\) 0.313613 2.62710i 0.0592674 0.496475i
\(29\) 0.700774i 0.130131i −0.997881 0.0650653i \(-0.979274\pi\)
0.997881 0.0650653i \(-0.0207256\pi\)
\(30\) 0 0
\(31\) 1.13725 + 0.656589i 0.204255 + 0.117927i 0.598639 0.801019i \(-0.295708\pi\)
−0.394383 + 0.918946i \(0.629042\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0 0
\(34\) 3.52215i 0.604043i
\(35\) 0 0
\(36\) 0 0
\(37\) 0.457320 + 0.792101i 0.0751829 + 0.130221i 0.901166 0.433475i \(-0.142713\pi\)
−0.825983 + 0.563695i \(0.809379\pi\)
\(38\) 1.77141 3.06818i 0.287361 0.497724i
\(39\) 0 0
\(40\) 0 0
\(41\) 4.88167 0.762388 0.381194 0.924495i \(-0.375513\pi\)
0.381194 + 0.924495i \(0.375513\pi\)
\(42\) 0 0
\(43\) 9.26963 1.41361 0.706803 0.707411i \(-0.250137\pi\)
0.706803 + 0.707411i \(0.250137\pi\)
\(44\) 1.38605 0.800236i 0.208955 0.120640i
\(45\) 0 0
\(46\) −1.61385 + 2.79527i −0.237949 + 0.412140i
\(47\) −1.33635 2.31462i −0.194926 0.337623i 0.751950 0.659220i \(-0.229113\pi\)
−0.946876 + 0.321598i \(0.895780\pi\)
\(48\) 0 0
\(49\) 4.82867 5.06793i 0.689810 0.723990i
\(50\) 0 0
\(51\) 0 0
\(52\) 0.667468 + 0.385363i 0.0925612 + 0.0534402i
\(53\) −8.04572 4.64520i −1.10516 0.638067i −0.167592 0.985856i \(-0.553599\pi\)
−0.937573 + 0.347789i \(0.886932\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.04195 2.43194i −0.139237 0.324982i
\(57\) 0 0
\(58\) −0.350387 0.606888i −0.0460081 0.0796883i
\(59\) 1.56198 2.70542i 0.203352 0.352216i −0.746254 0.665661i \(-0.768150\pi\)
0.949606 + 0.313445i \(0.101483\pi\)
\(60\) 0 0
\(61\) −9.43214 + 5.44565i −1.20766 + 0.697244i −0.962248 0.272175i \(-0.912257\pi\)
−0.245414 + 0.969418i \(0.578924\pi\)
\(62\) 1.31318 0.166774
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 3.40818 5.90314i 0.416375 0.721183i −0.579196 0.815188i \(-0.696634\pi\)
0.995572 + 0.0940048i \(0.0299669\pi\)
\(68\) −1.76107 3.05027i −0.213561 0.369899i
\(69\) 0 0
\(70\) 0 0
\(71\) 6.47930i 0.768951i 0.923135 + 0.384475i \(0.125618\pi\)
−0.923135 + 0.384475i \(0.874382\pi\)
\(72\) 0 0
\(73\) 9.55835 + 5.51852i 1.11872 + 0.645894i 0.941074 0.338201i \(-0.109818\pi\)
0.177647 + 0.984094i \(0.443152\pi\)
\(74\) 0.792101 + 0.457320i 0.0920799 + 0.0531623i
\(75\) 0 0
\(76\) 3.54282i 0.406390i
\(77\) 4.20460 + 0.501930i 0.479158 + 0.0572002i
\(78\) 0 0
\(79\) −1.45086 2.51296i −0.163234 0.282730i 0.772792 0.634659i \(-0.218859\pi\)
−0.936027 + 0.351928i \(0.885526\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 4.22765 2.44083i 0.466865 0.269545i
\(83\) −11.9777 −1.31472 −0.657361 0.753576i \(-0.728327\pi\)
−0.657361 + 0.753576i \(0.728327\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 8.02773 4.63481i 0.865653 0.499785i
\(87\) 0 0
\(88\) 0.800236 1.38605i 0.0853055 0.147753i
\(89\) 4.40369 + 7.62742i 0.466791 + 0.808505i 0.999280 0.0379313i \(-0.0120768\pi\)
−0.532490 + 0.846437i \(0.678743\pi\)
\(90\) 0 0
\(91\) 0.803059 + 1.87436i 0.0841835 + 0.196486i
\(92\) 3.22770i 0.336511i
\(93\) 0 0
\(94\) −2.31462 1.33635i −0.238735 0.137834i
\(95\) 0 0
\(96\) 0 0
\(97\) 5.31224i 0.539376i −0.962948 0.269688i \(-0.913079\pi\)
0.962948 0.269688i \(-0.0869206\pi\)
\(98\) 1.64779 6.80329i 0.166452 0.687236i
\(99\) 0 0
\(100\) 0 0
\(101\) −4.62663 + 8.01356i −0.460367 + 0.797379i −0.998979 0.0451749i \(-0.985615\pi\)
0.538612 + 0.842554i \(0.318949\pi\)
\(102\) 0 0
\(103\) 13.7055 7.91290i 1.35045 0.779681i 0.362136 0.932125i \(-0.382048\pi\)
0.988312 + 0.152444i \(0.0487144\pi\)
\(104\) 0.770726 0.0755759
\(105\) 0 0
\(106\) −9.29040 −0.902363
\(107\) 10.7514 6.20735i 1.03938 0.600087i 0.119724 0.992807i \(-0.461799\pi\)
0.919658 + 0.392720i \(0.128466\pi\)
\(108\) 0 0
\(109\) 5.51750 9.55659i 0.528480 0.915355i −0.470968 0.882150i \(-0.656095\pi\)
0.999449 0.0332048i \(-0.0105713\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −2.11833 1.58515i −0.200163 0.149782i
\(113\) 15.0301i 1.41391i −0.707256 0.706957i \(-0.750067\pi\)
0.707256 0.706957i \(-0.249933\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.606888 0.350387i −0.0563482 0.0325326i
\(117\) 0 0
\(118\) 3.12395i 0.287583i
\(119\) 1.10459 9.25303i 0.101258 0.848223i
\(120\) 0 0
\(121\) −4.21924 7.30795i −0.383568 0.664359i
\(122\) −5.44565 + 9.43214i −0.493026 + 0.853946i
\(123\) 0 0
\(124\) 1.13725 0.656589i 0.102128 0.0589634i
\(125\) 0 0
\(126\) 0 0
\(127\) −2.66506 −0.236486 −0.118243 0.992985i \(-0.537726\pi\)
−0.118243 + 0.992985i \(0.537726\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 0 0
\(131\) 7.10987 + 12.3147i 0.621192 + 1.07594i 0.989264 + 0.146139i \(0.0466848\pi\)
−0.368071 + 0.929797i \(0.619982\pi\)
\(132\) 0 0
\(133\) 5.61590 7.50486i 0.486960 0.650754i
\(134\) 6.81636i 0.588844i
\(135\) 0 0
\(136\) −3.05027 1.76107i −0.261558 0.151011i
\(137\) −0.112698 0.0650662i −0.00962843 0.00555898i 0.495178 0.868792i \(-0.335103\pi\)
−0.504806 + 0.863233i \(0.668436\pi\)
\(138\) 0 0
\(139\) 3.63572i 0.308378i 0.988041 + 0.154189i \(0.0492765\pi\)
−0.988041 + 0.154189i \(0.950724\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 3.23965 + 5.61123i 0.271865 + 0.470884i
\(143\) −0.616762 + 1.06826i −0.0515763 + 0.0893327i
\(144\) 0 0
\(145\) 0 0
\(146\) 11.0370 0.913432
\(147\) 0 0
\(148\) 0.914639 0.0751829
\(149\) −2.53957 + 1.46622i −0.208049 + 0.120117i −0.600405 0.799696i \(-0.704994\pi\)
0.392355 + 0.919814i \(0.371660\pi\)
\(150\) 0 0
\(151\) −3.56919 + 6.18201i −0.290456 + 0.503085i −0.973918 0.226902i \(-0.927140\pi\)
0.683461 + 0.729987i \(0.260474\pi\)
\(152\) −1.77141 3.06818i −0.143681 0.248862i
\(153\) 0 0
\(154\) 3.89225 1.66762i 0.313647 0.134380i
\(155\) 0 0
\(156\) 0 0
\(157\) −12.3963 7.15702i −0.989334 0.571192i −0.0842589 0.996444i \(-0.526852\pi\)
−0.905075 + 0.425252i \(0.860186\pi\)
\(158\) −2.51296 1.45086i −0.199921 0.115424i
\(159\) 0 0
\(160\) 0 0
\(161\) −5.11638 + 6.83732i −0.403227 + 0.538857i
\(162\) 0 0
\(163\) −3.60448 6.24313i −0.282324 0.489000i 0.689632 0.724160i \(-0.257772\pi\)
−0.971957 + 0.235159i \(0.924439\pi\)
\(164\) 2.44083 4.22765i 0.190597 0.330124i
\(165\) 0 0
\(166\) −10.3730 + 5.98884i −0.805099 + 0.464824i
\(167\) −13.8952 −1.07524 −0.537620 0.843187i \(-0.680677\pi\)
−0.537620 + 0.843187i \(0.680677\pi\)
\(168\) 0 0
\(169\) 12.4060 0.954306
\(170\) 0 0
\(171\) 0 0
\(172\) 4.63481 8.02773i 0.353401 0.612109i
\(173\) 1.18370 + 2.05023i 0.0899951 + 0.155876i 0.907509 0.420033i \(-0.137982\pi\)
−0.817514 + 0.575909i \(0.804648\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.60047i 0.120640i
\(177\) 0 0
\(178\) 7.62742 + 4.40369i 0.571700 + 0.330071i
\(179\) −15.4837 8.93953i −1.15731 0.668172i −0.206650 0.978415i \(-0.566256\pi\)
−0.950657 + 0.310243i \(0.899590\pi\)
\(180\) 0 0
\(181\) 16.6673i 1.23887i 0.785049 + 0.619434i \(0.212638\pi\)
−0.785049 + 0.619434i \(0.787362\pi\)
\(182\) 1.63265 + 1.22171i 0.121020 + 0.0905594i
\(183\) 0 0
\(184\) 1.61385 + 2.79527i 0.118975 + 0.206070i
\(185\) 0 0
\(186\) 0 0
\(187\) 4.88187 2.81855i 0.356998 0.206113i
\(188\) −2.67270 −0.194926
\(189\) 0 0
\(190\) 0 0
\(191\) −21.4359 + 12.3760i −1.55104 + 0.895496i −0.552987 + 0.833190i \(0.686512\pi\)
−0.998057 + 0.0623063i \(0.980154\pi\)
\(192\) 0 0
\(193\) 6.28835 10.8917i 0.452645 0.784005i −0.545904 0.837848i \(-0.683814\pi\)
0.998549 + 0.0538428i \(0.0171470\pi\)
\(194\) −2.65612 4.60054i −0.190698 0.330299i
\(195\) 0 0
\(196\) −1.97462 6.71572i −0.141044 0.479694i
\(197\) 19.7360i 1.40613i −0.711125 0.703066i \(-0.751814\pi\)
0.711125 0.703066i \(-0.248186\pi\)
\(198\) 0 0
\(199\) 9.82275 + 5.67117i 0.696316 + 0.402018i 0.805974 0.591951i \(-0.201642\pi\)
−0.109658 + 0.993969i \(0.534975\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 9.25326i 0.651057i
\(203\) −0.730173 1.70424i −0.0512481 0.119614i
\(204\) 0 0
\(205\) 0 0
\(206\) 7.91290 13.7055i 0.551318 0.954911i
\(207\) 0 0
\(208\) 0.667468 0.385363i 0.0462806 0.0267201i
\(209\) 5.67019 0.392215
\(210\) 0 0
\(211\) 16.0647 1.10594 0.552970 0.833201i \(-0.313494\pi\)
0.552970 + 0.833201i \(0.313494\pi\)
\(212\) −8.04572 + 4.64520i −0.552582 + 0.319034i
\(213\) 0 0
\(214\) 6.20735 10.7514i 0.424326 0.734954i
\(215\) 0 0
\(216\) 0 0
\(217\) 3.44985 + 0.411830i 0.234191 + 0.0279569i
\(218\) 11.0350i 0.747384i
\(219\) 0 0
\(220\) 0 0
\(221\) 2.35092 + 1.35730i 0.158140 + 0.0913022i
\(222\) 0 0
\(223\) 2.00917i 0.134544i 0.997735 + 0.0672720i \(0.0214295\pi\)
−0.997735 + 0.0672720i \(0.978570\pi\)
\(224\) −2.62710 0.313613i −0.175530 0.0209542i
\(225\) 0 0
\(226\) −7.51506 13.0165i −0.499894 0.865842i
\(227\) −1.95288 + 3.38249i −0.129617 + 0.224504i −0.923528 0.383530i \(-0.874708\pi\)
0.793911 + 0.608034i \(0.208042\pi\)
\(228\) 0 0
\(229\) 11.5904 6.69174i 0.765918 0.442203i −0.0654987 0.997853i \(-0.520864\pi\)
0.831416 + 0.555650i \(0.187530\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −0.700774 −0.0460081
\(233\) −8.91673 + 5.14808i −0.584154 + 0.337262i −0.762783 0.646655i \(-0.776167\pi\)
0.178628 + 0.983917i \(0.442834\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −1.56198 2.70542i −0.101676 0.176108i
\(237\) 0 0
\(238\) −3.66991 8.56565i −0.237885 0.555229i
\(239\) 17.5460i 1.13495i −0.823389 0.567477i \(-0.807920\pi\)
0.823389 0.567477i \(-0.192080\pi\)
\(240\) 0 0
\(241\) 8.66068 + 5.00024i 0.557883 + 0.322094i 0.752295 0.658826i \(-0.228947\pi\)
−0.194412 + 0.980920i \(0.562280\pi\)
\(242\) −7.30795 4.21924i −0.469773 0.271223i
\(243\) 0 0
\(244\) 10.8913i 0.697244i
\(245\) 0 0
\(246\) 0 0
\(247\) 1.36527 + 2.36472i 0.0868702 + 0.150464i
\(248\) 0.656589 1.13725i 0.0416935 0.0722152i
\(249\) 0 0
\(250\) 0 0
\(251\) 3.55412 0.224334 0.112167 0.993689i \(-0.464221\pi\)
0.112167 + 0.993689i \(0.464221\pi\)
\(252\) 0 0
\(253\) −5.16584 −0.324774
\(254\) −2.30801 + 1.33253i −0.144818 + 0.0836105i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −3.55507 6.15756i −0.221759 0.384098i 0.733583 0.679600i \(-0.237847\pi\)
−0.955342 + 0.295502i \(0.904513\pi\)
\(258\) 0 0
\(259\) 1.93751 + 1.44984i 0.120391 + 0.0900885i
\(260\) 0 0
\(261\) 0 0
\(262\) 12.3147 + 7.10987i 0.760802 + 0.439249i
\(263\) 24.7253 + 14.2752i 1.52463 + 0.880245i 0.999574 + 0.0291760i \(0.00928833\pi\)
0.525054 + 0.851069i \(0.324045\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 1.11108 9.30735i 0.0681245 0.570670i
\(267\) 0 0
\(268\) −3.40818 5.90314i −0.208188 0.360592i
\(269\) −12.9628 + 22.4523i −0.790359 + 1.36894i 0.135386 + 0.990793i \(0.456772\pi\)
−0.925745 + 0.378149i \(0.876561\pi\)
\(270\) 0 0
\(271\) −24.1643 + 13.9513i −1.46788 + 0.847479i −0.999353 0.0359726i \(-0.988547\pi\)
−0.468523 + 0.883451i \(0.655214\pi\)
\(272\) −3.52215 −0.213561
\(273\) 0 0
\(274\) −0.130132 −0.00786158
\(275\) 0 0
\(276\) 0 0
\(277\) 5.18485 8.98042i 0.311527 0.539581i −0.667166 0.744909i \(-0.732493\pi\)
0.978693 + 0.205328i \(0.0658261\pi\)
\(278\) 1.81786 + 3.14863i 0.109028 + 0.188842i
\(279\) 0 0
\(280\) 0 0
\(281\) 21.0412i 1.25521i 0.778530 + 0.627607i \(0.215965\pi\)
−0.778530 + 0.627607i \(0.784035\pi\)
\(282\) 0 0
\(283\) 23.7046 + 13.6859i 1.40909 + 0.813541i 0.995301 0.0968293i \(-0.0308701\pi\)
0.413794 + 0.910371i \(0.364203\pi\)
\(284\) 5.61123 + 3.23965i 0.332965 + 0.192238i
\(285\) 0 0
\(286\) 1.23352i 0.0729399i
\(287\) 11.8719 5.08646i 0.700777 0.300244i
\(288\) 0 0
\(289\) 2.29724 + 3.97894i 0.135132 + 0.234055i
\(290\) 0 0
\(291\) 0 0
\(292\) 9.55835 5.51852i 0.559360 0.322947i
\(293\) −16.9059 −0.987654 −0.493827 0.869560i \(-0.664402\pi\)
−0.493827 + 0.869560i \(0.664402\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.792101 0.457320i 0.0460399 0.0265812i
\(297\) 0 0
\(298\) −1.46622 + 2.53957i −0.0849358 + 0.147113i
\(299\) −1.24384 2.15439i −0.0719328 0.124591i
\(300\) 0 0
\(301\) 22.5432 9.65851i 1.29937 0.556707i
\(302\) 7.13837i 0.410767i
\(303\) 0 0
\(304\) −3.06818 1.77141i −0.175972 0.101597i
\(305\) 0 0
\(306\) 0 0
\(307\) 14.0139i 0.799813i 0.916556 + 0.399906i \(0.130957\pi\)
−0.916556 + 0.399906i \(0.869043\pi\)
\(308\) 2.53698 3.39032i 0.144558 0.193182i
\(309\) 0 0
\(310\) 0 0
\(311\) 6.72211 11.6430i 0.381176 0.660216i −0.610055 0.792359i \(-0.708853\pi\)
0.991231 + 0.132143i \(0.0421859\pi\)
\(312\) 0 0
\(313\) −3.68760 + 2.12904i −0.208436 + 0.120340i −0.600584 0.799562i \(-0.705065\pi\)
0.392149 + 0.919902i \(0.371732\pi\)
\(314\) −14.3140 −0.807788
\(315\) 0 0
\(316\) −2.90172 −0.163234
\(317\) 0.171111 0.0987910i 0.00961055 0.00554866i −0.495187 0.868786i \(-0.664900\pi\)
0.504798 + 0.863238i \(0.331567\pi\)
\(318\) 0 0
\(319\) 0.560785 0.971308i 0.0313979 0.0543828i
\(320\) 0 0
\(321\) 0 0
\(322\) −1.01225 + 8.47948i −0.0564105 + 0.472543i
\(323\) 12.4783i 0.694314i
\(324\) 0 0
\(325\) 0 0
\(326\) −6.24313 3.60448i −0.345775 0.199633i
\(327\) 0 0
\(328\) 4.88167i 0.269545i
\(329\) −5.66165 4.23662i −0.312137 0.233572i
\(330\) 0 0
\(331\) −2.29740 3.97922i −0.126277 0.218718i 0.795955 0.605356i \(-0.206969\pi\)
−0.922231 + 0.386639i \(0.873636\pi\)
\(332\) −5.98884 + 10.3730i −0.328680 + 0.569291i
\(333\) 0 0
\(334\) −12.0336 + 6.94758i −0.658447 + 0.380155i
\(335\) 0 0
\(336\) 0 0
\(337\) −6.05076 −0.329606 −0.164803 0.986327i \(-0.552699\pi\)
−0.164803 + 0.986327i \(0.552699\pi\)
\(338\) 10.7439 6.20299i 0.584391 0.337398i
\(339\) 0 0
\(340\) 0 0
\(341\) 1.05085 + 1.82013i 0.0569069 + 0.0985656i
\(342\) 0 0
\(343\) 6.46250 17.3562i 0.348942 0.937144i
\(344\) 9.26963i 0.499785i
\(345\) 0 0
\(346\) 2.05023 + 1.18370i 0.110221 + 0.0636362i
\(347\) −2.75573 1.59102i −0.147935 0.0854104i 0.424205 0.905566i \(-0.360553\pi\)
−0.572140 + 0.820156i \(0.693887\pi\)
\(348\) 0 0
\(349\) 29.0573i 1.55540i 0.628636 + 0.777700i \(0.283614\pi\)
−0.628636 + 0.777700i \(0.716386\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.800236 1.38605i −0.0426527 0.0738767i
\(353\) 3.83327 6.63942i 0.204025 0.353381i −0.745797 0.666173i \(-0.767931\pi\)
0.949822 + 0.312792i \(0.101264\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 8.80739 0.466791
\(357\) 0 0
\(358\) −17.8791 −0.944938
\(359\) −19.6694 + 11.3561i −1.03811 + 0.599353i −0.919297 0.393564i \(-0.871242\pi\)
−0.118812 + 0.992917i \(0.537909\pi\)
\(360\) 0 0
\(361\) −3.22420 + 5.58447i −0.169695 + 0.293920i
\(362\) 8.33363 + 14.4343i 0.438006 + 0.758649i
\(363\) 0 0
\(364\) 2.02477 + 0.241710i 0.106127 + 0.0126690i
\(365\) 0 0
\(366\) 0 0
\(367\) −16.2368 9.37433i −0.847555 0.489336i 0.0122703 0.999925i \(-0.496094\pi\)
−0.859825 + 0.510589i \(0.829427\pi\)
\(368\) 2.79527 + 1.61385i 0.145713 + 0.0841277i
\(369\) 0 0
\(370\) 0 0
\(371\) −24.4068 2.91359i −1.26714 0.151266i
\(372\) 0 0
\(373\) −1.42057 2.46050i −0.0735545 0.127400i 0.826902 0.562346i \(-0.190101\pi\)
−0.900457 + 0.434946i \(0.856768\pi\)
\(374\) 2.81855 4.88187i 0.145744 0.252435i
\(375\) 0 0
\(376\) −2.31462 + 1.33635i −0.119368 + 0.0689169i
\(377\) 0.540105 0.0278168
\(378\) 0 0
\(379\) −27.2750 −1.40102 −0.700510 0.713642i \(-0.747044\pi\)
−0.700510 + 0.713642i \(0.747044\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −12.3760 + 21.4359i −0.633211 + 1.09675i
\(383\) 15.1175 + 26.1843i 0.772469 + 1.33796i 0.936206 + 0.351451i \(0.114312\pi\)
−0.163737 + 0.986504i \(0.552355\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 12.5767i 0.640137i
\(387\) 0 0
\(388\) −4.60054 2.65612i −0.233557 0.134844i
\(389\) 4.29588 + 2.48023i 0.217810 + 0.125752i 0.604936 0.796274i \(-0.293199\pi\)
−0.387126 + 0.922027i \(0.626532\pi\)
\(390\) 0 0
\(391\) 11.3684i 0.574926i
\(392\) −5.06793 4.82867i −0.255969 0.243885i
\(393\) 0 0
\(394\) −9.86800 17.0919i −0.497143 0.861077i
\(395\) 0 0
\(396\) 0 0
\(397\) 12.6477 7.30213i 0.634768 0.366483i −0.147828 0.989013i \(-0.547228\pi\)
0.782596 + 0.622530i \(0.213895\pi\)
\(398\) 11.3423 0.568540
\(399\) 0 0
\(400\) 0 0
\(401\) −17.5622 + 10.1395i −0.877014 + 0.506345i −0.869673 0.493629i \(-0.835670\pi\)
−0.00734158 + 0.999973i \(0.502337\pi\)
\(402\) 0 0
\(403\) −0.506050 + 0.876505i −0.0252082 + 0.0436618i
\(404\) 4.62663 + 8.01356i 0.230183 + 0.398689i
\(405\) 0 0
\(406\) −1.48447 1.11083i −0.0736730 0.0551296i
\(407\) 1.46385i 0.0725606i
\(408\) 0 0
\(409\) 4.26877 + 2.46458i 0.211077 + 0.121865i 0.601812 0.798638i \(-0.294446\pi\)
−0.390735 + 0.920503i \(0.627779\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 15.8258i 0.779681i
\(413\) 0.979714 8.20693i 0.0482086 0.403837i
\(414\) 0 0
\(415\) 0 0
\(416\) 0.385363 0.667468i 0.0188940 0.0327253i
\(417\) 0 0
\(418\) 4.91053 2.83510i 0.240182 0.138669i
\(419\) −24.0686 −1.17583 −0.587913 0.808924i \(-0.700050\pi\)
−0.587913 + 0.808924i \(0.700050\pi\)
\(420\) 0 0
\(421\) 16.0657 0.782995 0.391498 0.920179i \(-0.371957\pi\)
0.391498 + 0.920179i \(0.371957\pi\)
\(422\) 13.9125 8.03236i 0.677248 0.391009i
\(423\) 0 0
\(424\) −4.64520 + 8.04572i −0.225591 + 0.390735i
\(425\) 0 0
\(426\) 0 0
\(427\) −17.2643 + 23.0713i −0.835478 + 1.11650i
\(428\) 12.4147i 0.600087i
\(429\) 0 0
\(430\) 0 0
\(431\) −0.373691 0.215751i −0.0180001 0.0103923i 0.490973 0.871175i \(-0.336641\pi\)
−0.508973 + 0.860782i \(0.669975\pi\)
\(432\) 0 0
\(433\) 30.5287i 1.46711i 0.679628 + 0.733557i \(0.262141\pi\)
−0.679628 + 0.733557i \(0.737859\pi\)
\(434\) 3.19357 1.36827i 0.153296 0.0656790i
\(435\) 0 0
\(436\) −5.51750 9.55659i −0.264240 0.457677i
\(437\) −5.71759 + 9.90315i −0.273509 + 0.473732i
\(438\) 0 0
\(439\) −32.9059 + 18.9982i −1.57051 + 0.906735i −0.574406 + 0.818571i \(0.694767\pi\)
−0.996106 + 0.0881648i \(0.971900\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 2.71461 0.129121
\(443\) −20.1789 + 11.6503i −0.958728 + 0.553522i −0.895781 0.444495i \(-0.853383\pi\)
−0.0629464 + 0.998017i \(0.520050\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 1.00459 + 1.73999i 0.0475685 + 0.0823911i
\(447\) 0 0
\(448\) −2.43194 + 1.04195i −0.114898 + 0.0492276i
\(449\) 21.9119i 1.03409i 0.855960 + 0.517043i \(0.172967\pi\)
−0.855960 + 0.517043i \(0.827033\pi\)
\(450\) 0 0
\(451\) 6.76623 + 3.90648i 0.318609 + 0.183949i
\(452\) −13.0165 7.51506i −0.612243 0.353479i
\(453\) 0 0
\(454\) 3.90576i 0.183306i
\(455\) 0 0
\(456\) 0 0
\(457\) 19.6821 + 34.0904i 0.920691 + 1.59468i 0.798349 + 0.602195i \(0.205707\pi\)
0.122341 + 0.992488i \(0.460960\pi\)
\(458\) 6.69174 11.5904i 0.312685 0.541586i
\(459\) 0 0
\(460\) 0 0
\(461\) 2.35282 0.109582 0.0547909 0.998498i \(-0.482551\pi\)
0.0547909 + 0.998498i \(0.482551\pi\)
\(462\) 0 0
\(463\) 2.24550 0.104357 0.0521787 0.998638i \(-0.483383\pi\)
0.0521787 + 0.998638i \(0.483383\pi\)
\(464\) −0.606888 + 0.350387i −0.0281741 + 0.0162663i
\(465\) 0 0
\(466\) −5.14808 + 8.91673i −0.238480 + 0.413059i
\(467\) −16.0931 27.8740i −0.744699 1.28986i −0.950335 0.311228i \(-0.899260\pi\)
0.205636 0.978628i \(-0.434074\pi\)
\(468\) 0 0
\(469\) 2.13770 17.9072i 0.0987099 0.826880i
\(470\) 0 0
\(471\) 0 0
\(472\) −2.70542 1.56198i −0.124527 0.0718958i
\(473\) 12.8482 + 7.41789i 0.590759 + 0.341075i
\(474\) 0 0
\(475\) 0 0
\(476\) −7.46106 5.58312i −0.341977 0.255902i
\(477\) 0 0
\(478\) −8.77298 15.1952i −0.401267 0.695014i
\(479\) −3.30556 + 5.72539i −0.151035 + 0.261600i −0.931608 0.363464i \(-0.881594\pi\)
0.780573 + 0.625064i \(0.214927\pi\)
\(480\) 0 0
\(481\) −0.610493 + 0.352468i −0.0278361 + 0.0160712i
\(482\) 10.0005 0.455510
\(483\) 0 0
\(484\) −8.43849 −0.383568
\(485\) 0 0
\(486\) 0 0
\(487\) 2.88167 4.99120i 0.130581 0.226173i −0.793320 0.608805i \(-0.791649\pi\)
0.923901 + 0.382632i \(0.124982\pi\)
\(488\) 5.44565 + 9.43214i 0.246513 + 0.426973i
\(489\) 0 0
\(490\) 0 0
\(491\) 2.90529i 0.131114i −0.997849 0.0655570i \(-0.979118\pi\)
0.997849 0.0655570i \(-0.0208824\pi\)
\(492\) 0 0
\(493\) −2.13755 1.23411i −0.0962704 0.0555817i
\(494\) 2.36472 + 1.36527i 0.106394 + 0.0614265i
\(495\) 0 0
\(496\) 1.31318i 0.0589634i
\(497\) 6.75111 + 15.7573i 0.302829 + 0.706810i
\(498\) 0 0
\(499\) −1.14104 1.97634i −0.0510800 0.0884732i 0.839355 0.543584i \(-0.182933\pi\)
−0.890435 + 0.455111i \(0.849600\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 3.07796 1.77706i 0.137376 0.0793141i
\(503\) −1.32664 −0.0591520 −0.0295760 0.999563i \(-0.509416\pi\)
−0.0295760 + 0.999563i \(0.509416\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −4.47375 + 2.58292i −0.198882 + 0.114825i
\(507\) 0 0
\(508\) −1.33253 + 2.30801i −0.0591215 + 0.102402i
\(509\) 21.5053 + 37.2483i 0.953207 + 1.65100i 0.738419 + 0.674342i \(0.235573\pi\)
0.214788 + 0.976661i \(0.431094\pi\)
\(510\) 0 0
\(511\) 28.9954 + 3.46136i 1.28268 + 0.153122i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −6.15756 3.55507i −0.271598 0.156807i
\(515\) 0 0
\(516\) 0 0
\(517\) 4.27758i 0.188128i
\(518\) 2.40285 + 0.286843i 0.105575 + 0.0126032i
\(519\) 0 0
\(520\) 0 0
\(521\) 19.8838 34.4397i 0.871124 1.50883i 0.0102890 0.999947i \(-0.496725\pi\)
0.860835 0.508884i \(-0.169942\pi\)
\(522\) 0 0
\(523\) −34.4338 + 19.8804i −1.50568 + 0.869307i −0.505706 + 0.862706i \(0.668768\pi\)
−0.999978 + 0.00660128i \(0.997899\pi\)
\(524\) 14.2197 0.621192
\(525\) 0 0
\(526\) 28.5503 1.24485
\(527\) 4.00555 2.31260i 0.174484 0.100739i
\(528\) 0 0
\(529\) −6.29098 + 10.8963i −0.273521 + 0.473752i
\(530\) 0 0
\(531\) 0 0
\(532\) −3.69145 8.61594i −0.160045 0.373548i
\(533\) 3.76242i 0.162969i
\(534\) 0 0
\(535\) 0 0
\(536\) −5.90314 3.40818i −0.254977 0.147211i
\(537\) 0 0
\(538\) 25.9257i 1.11774i
\(539\) 10.7483 3.16033i 0.462963 0.136125i
\(540\) 0 0
\(541\) −10.1006 17.4947i −0.434258 0.752157i 0.562977 0.826473i \(-0.309656\pi\)
−0.997235 + 0.0743161i \(0.976323\pi\)
\(542\) −13.9513 + 24.1643i −0.599258 + 1.03795i
\(543\) 0 0
\(544\) −3.05027 + 1.76107i −0.130779 + 0.0755054i
\(545\) 0 0
\(546\) 0 0
\(547\) −34.5631 −1.47781 −0.738905 0.673810i \(-0.764657\pi\)
−0.738905 + 0.673810i \(0.764657\pi\)
\(548\) −0.112698 + 0.0650662i −0.00481422 + 0.00277949i
\(549\) 0 0
\(550\) 0 0
\(551\) −1.24136 2.15010i −0.0528837 0.0915973i
\(552\) 0 0
\(553\) −6.14679 4.59965i −0.261388 0.195597i
\(554\) 10.3697i 0.440566i
\(555\) 0 0
\(556\) 3.14863 + 1.81786i 0.133532 + 0.0770945i
\(557\) 28.1278 + 16.2396i 1.19181 + 0.688094i 0.958718 0.284360i \(-0.0917811\pi\)
0.233096 + 0.972454i \(0.425114\pi\)
\(558\) 0 0
\(559\) 7.14434i 0.302173i
\(560\) 0 0
\(561\) 0 0
\(562\) 10.5206 + 18.2222i 0.443785 + 0.768658i
\(563\) −7.19395 + 12.4603i −0.303189 + 0.525139i −0.976856 0.213896i \(-0.931385\pi\)
0.673668 + 0.739035i \(0.264718\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 27.3718 1.15052
\(567\) 0 0
\(568\) 6.47930 0.271865
\(569\) 6.84504 3.95199i 0.286959 0.165676i −0.349611 0.936895i \(-0.613686\pi\)
0.636570 + 0.771219i \(0.280353\pi\)
\(570\) 0 0
\(571\) 18.3198 31.7309i 0.766661 1.32789i −0.172704 0.984974i \(-0.555250\pi\)
0.939364 0.342921i \(-0.111416\pi\)
\(572\) 0.616762 + 1.06826i 0.0257881 + 0.0446664i
\(573\) 0 0
\(574\) 7.73815 10.3410i 0.322984 0.431624i
\(575\) 0 0
\(576\) 0 0
\(577\) −20.2583 11.6961i −0.843363 0.486916i 0.0150431 0.999887i \(-0.495211\pi\)
−0.858406 + 0.512971i \(0.828545\pi\)
\(578\) 3.97894 + 2.29724i 0.165502 + 0.0955527i
\(579\) 0 0
\(580\) 0 0
\(581\) −29.1290 + 12.4802i −1.20848 + 0.517765i
\(582\) 0 0
\(583\) −7.43451 12.8770i −0.307906 0.533309i
\(584\) 5.51852 9.55835i 0.228358 0.395527i
\(585\) 0 0
\(586\) −14.6409 + 8.45295i −0.604812 + 0.349188i
\(587\) −23.7776 −0.981407 −0.490704 0.871327i \(-0.663260\pi\)
−0.490704 + 0.871327i \(0.663260\pi\)
\(588\) 0 0
\(589\) 4.65236 0.191697
\(590\) 0 0
\(591\) 0 0
\(592\) 0.457320 0.792101i 0.0187957 0.0325551i
\(593\) 19.4555 + 33.6979i 0.798942 + 1.38381i 0.920306 + 0.391200i \(0.127940\pi\)
−0.121364 + 0.992608i \(0.538727\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 2.93244i 0.120117i
\(597\) 0 0
\(598\) −2.15439 1.24384i −0.0880994 0.0508642i
\(599\) 3.09380 + 1.78621i 0.126409 + 0.0729824i 0.561871 0.827225i \(-0.310082\pi\)
−0.435462 + 0.900207i \(0.643415\pi\)
\(600\) 0 0
\(601\) 21.3183i 0.869591i −0.900529 0.434795i \(-0.856821\pi\)
0.900529 0.434795i \(-0.143179\pi\)
\(602\) 14.6937 19.6361i 0.598871 0.800308i
\(603\) 0 0
\(604\) 3.56919 + 6.18201i 0.145228 + 0.251543i
\(605\) 0 0
\(606\) 0 0
\(607\) 0.494331 0.285402i 0.0200643 0.0115841i −0.489934 0.871759i \(-0.662979\pi\)
0.509999 + 0.860175i \(0.329646\pi\)
\(608\) −3.54282 −0.143681
\(609\) 0 0
\(610\) 0 0
\(611\) 1.78394 1.02996i 0.0721705 0.0416676i
\(612\) 0 0
\(613\) −17.0869 + 29.5954i −0.690134 + 1.19535i 0.281659 + 0.959514i \(0.409115\pi\)
−0.971794 + 0.235833i \(0.924218\pi\)
\(614\) 7.00693 + 12.1364i 0.282777 + 0.489783i
\(615\) 0 0
\(616\) 0.501930 4.20460i 0.0202233 0.169408i
\(617\) 20.1713i 0.812066i 0.913858 + 0.406033i \(0.133088\pi\)
−0.913858 + 0.406033i \(0.866912\pi\)
\(618\) 0 0
\(619\) 13.9621 + 8.06104i 0.561186 + 0.324001i 0.753621 0.657309i \(-0.228305\pi\)
−0.192436 + 0.981310i \(0.561639\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 13.4442i 0.539064i
\(623\) 18.6569 + 13.9610i 0.747474 + 0.559336i
\(624\) 0 0
\(625\) 0 0
\(626\) −2.12904 + 3.68760i −0.0850935 + 0.147386i
\(627\) 0 0
\(628\) −12.3963 + 7.15702i −0.494667 + 0.285596i
\(629\) 3.22149 0.128449
\(630\) 0 0
\(631\) 3.10655 0.123670 0.0618350 0.998086i \(-0.480305\pi\)
0.0618350 + 0.998086i \(0.480305\pi\)
\(632\) −2.51296 + 1.45086i −0.0999603 + 0.0577121i
\(633\) 0 0
\(634\) 0.0987910 0.171111i 0.00392349 0.00679569i
\(635\) 0 0
\(636\) 0 0
\(637\) 3.90598 + 3.72158i 0.154761 + 0.147454i
\(638\) 1.12157i 0.0444034i
\(639\) 0 0
\(640\) 0 0
\(641\) 18.9248 + 10.9262i 0.747483 + 0.431559i 0.824784 0.565448i \(-0.191297\pi\)
−0.0773008 + 0.997008i \(0.524630\pi\)
\(642\) 0 0
\(643\) 25.4873i 1.00512i 0.864542 + 0.502560i \(0.167609\pi\)
−0.864542 + 0.502560i \(0.832391\pi\)
\(644\) 3.36311 + 7.84957i 0.132525 + 0.309317i
\(645\) 0 0
\(646\) −6.23917 10.8066i −0.245477 0.425179i
\(647\) 24.0030 41.5745i 0.943657 1.63446i 0.185239 0.982694i \(-0.440694\pi\)
0.758418 0.651768i \(-0.225973\pi\)
\(648\) 0 0
\(649\) 4.32995 2.49990i 0.169966 0.0981296i
\(650\) 0 0
\(651\) 0 0
\(652\) −7.20895 −0.282324
\(653\) −39.8741 + 23.0213i −1.56039 + 0.900894i −0.563177 + 0.826336i \(0.690421\pi\)
−0.997217 + 0.0745575i \(0.976246\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −2.44083 4.22765i −0.0952985 0.165062i
\(657\) 0 0
\(658\) −7.02144 0.838194i −0.273724 0.0326762i
\(659\) 14.8751i 0.579453i −0.957109 0.289727i \(-0.906436\pi\)
0.957109 0.289727i \(-0.0935644\pi\)
\(660\) 0 0
\(661\) 36.7957 + 21.2440i 1.43119 + 0.826296i 0.997211 0.0746297i \(-0.0237775\pi\)
0.433974 + 0.900925i \(0.357111\pi\)
\(662\) −3.97922 2.29740i −0.154657 0.0892911i
\(663\) 0 0
\(664\) 11.9777i 0.464824i
\(665\) 0 0
\(666\) 0 0
\(667\) 1.13094 + 1.95885i 0.0437903 + 0.0758471i
\(668\) −6.94758 + 12.0336i −0.268810 + 0.465593i
\(669\) 0 0
\(670\) 0 0
\(671\) −17.4312 −0.672925
\(672\) 0 0
\(673\) −50.6101 −1.95088 −0.975439 0.220270i \(-0.929306\pi\)
−0.975439 + 0.220270i \(0.929306\pi\)
\(674\) −5.24011 + 3.02538i −0.201841 + 0.116533i
\(675\) 0 0
\(676\) 6.20299 10.7439i 0.238577 0.413227i
\(677\) 17.2777 + 29.9259i 0.664037 + 1.15015i 0.979545 + 0.201223i \(0.0644916\pi\)
−0.315508 + 0.948923i \(0.602175\pi\)
\(678\) 0 0
\(679\) −5.53510 12.9191i −0.212418 0.495788i
\(680\) 0 0
\(681\) 0 0
\(682\) 1.82013 + 1.05085i 0.0696964 + 0.0402392i
\(683\) 14.8563 + 8.57731i 0.568462 + 0.328202i 0.756535 0.653953i \(-0.226891\pi\)
−0.188073 + 0.982155i \(0.560224\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −3.08138 18.2621i −0.117648 0.697251i
\(687\) 0 0
\(688\) −4.63481 8.02773i −0.176701 0.306055i
\(689\) 3.58017 6.20104i 0.136394 0.236241i
\(690\) 0 0
\(691\) −30.8635 + 17.8190i −1.17410 + 0.677869i −0.954643 0.297753i \(-0.903763\pi\)
−0.219460 + 0.975622i \(0.570429\pi\)
\(692\) 2.36740 0.0899951
\(693\) 0 0
\(694\) −3.18204 −0.120788
\(695\) 0 0
\(696\) 0 0
\(697\) 8.59697 14.8904i 0.325633 0.564014i
\(698\) 14.5286 + 25.1643i 0.549917 + 0.952484i
\(699\) 0 0
\(700\) 0 0
\(701\) 23.0808i 0.871751i −0.900007 0.435876i \(-0.856439\pi\)
0.900007 0.435876i \(-0.143561\pi\)
\(702\) 0 0
\(703\) 2.80627 + 1.62020i 0.105841 + 0.0611071i
\(704\) −1.38605 0.800236i −0.0522387 0.0301600i
\(705\) 0 0
\(706\) 7.66655i 0.288534i
\(707\) −2.90195 + 24.3092i −0.109139 + 0.914243i
\(708\) 0 0
\(709\) −4.08362 7.07303i −0.153363 0.265633i 0.779098 0.626902i \(-0.215677\pi\)
−0.932462 + 0.361268i \(0.882344\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 7.62742 4.40369i 0.285850 0.165035i
\(713\) −4.23854 −0.158735
\(714\) 0 0
\(715\) 0 0
\(716\) −15.4837 + 8.93953i −0.578654 + 0.334086i
\(717\) 0 0
\(718\) −11.3561 + 19.6694i −0.423806 + 0.734054i
\(719\) 0.377499 + 0.653847i 0.0140783 + 0.0243844i 0.872979 0.487758i \(-0.162185\pi\)
−0.858900 + 0.512143i \(0.828852\pi\)
\(720\) 0 0
\(721\) 25.0862 33.5242i 0.934260 1.24851i
\(722\) 6.44839i 0.239984i
\(723\) 0 0
\(724\) 14.4343 + 8.33363i 0.536446 + 0.309717i
\(725\) 0 0
\(726\) 0 0
\(727\) 4.27807i 0.158665i 0.996848 + 0.0793325i \(0.0252789\pi\)
−0.996848 + 0.0793325i \(0.974721\pi\)
\(728\) 1.87436 0.803059i 0.0694684 0.0297634i
\(729\) 0 0
\(730\) 0 0
\(731\) 16.3245 28.2749i 0.603783 1.04578i
\(732\) 0 0
\(733\) −29.0656 + 16.7810i −1.07356 + 0.619822i −0.929153 0.369696i \(-0.879462\pi\)
−0.144410 + 0.989518i \(0.546129\pi\)
\(734\) −18.7487 −0.692026
\(735\) 0 0
\(736\) 3.22770 0.118975
\(737\) 9.44781 5.45470i 0.348015 0.200926i
\(738\) 0 0
\(739\) −17.3726 + 30.0902i −0.639060 + 1.10688i 0.346579 + 0.938021i \(0.387343\pi\)
−0.985639 + 0.168864i \(0.945990\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −22.5937 + 9.68015i −0.829441 + 0.355369i
\(743\) 14.3040i 0.524762i 0.964964 + 0.262381i \(0.0845077\pi\)
−0.964964 + 0.262381i \(0.915492\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −2.46050 1.42057i −0.0900854 0.0520109i
\(747\) 0 0
\(748\) 5.63710i 0.206113i
\(749\) 19.6791 26.2984i 0.719060 0.960923i
\(750\) 0 0
\(751\) −21.3172 36.9224i −0.777874 1.34732i −0.933165 0.359449i \(-0.882965\pi\)
0.155290 0.987869i \(-0.450369\pi\)
\(752\) −1.33635 + 2.31462i −0.0487316 + 0.0844056i
\(753\) 0 0
\(754\) 0.467744 0.270052i 0.0170342 0.00983473i
\(755\) 0 0
\(756\) 0 0
\(757\) −2.92253 −0.106221 −0.0531107 0.998589i \(-0.516914\pi\)
−0.0531107 + 0.998589i \(0.516914\pi\)
\(758\) −23.6208 + 13.6375i −0.857946 + 0.495336i
\(759\) 0 0
\(760\) 0 0
\(761\) 15.2447 + 26.4046i 0.552621 + 0.957167i 0.998084 + 0.0618669i \(0.0197054\pi\)
−0.445464 + 0.895300i \(0.646961\pi\)
\(762\) 0 0
\(763\) 3.46072 28.9900i 0.125287 1.04951i
\(764\) 24.7520i 0.895496i
\(765\) 0 0
\(766\) 26.1843 + 15.1175i 0.946077 + 0.546218i
\(767\) 2.08514 + 1.20386i 0.0752900 + 0.0434687i
\(768\) 0 0
\(769\) 42.7989i 1.54337i −0.636005 0.771685i \(-0.719414\pi\)
0.636005 0.771685i \(-0.280586\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −6.28835 10.8917i −0.226323 0.392002i
\(773\) 20.1996 34.9867i 0.726529 1.25838i −0.231813 0.972760i \(-0.574466\pi\)
0.958342 0.285624i \(-0.0922010\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −5.31224 −0.190698
\(777\) 0 0
\(778\) 4.96045 0.177841
\(779\) 14.9778 8.64744i 0.536636 0.309827i
\(780\) 0 0
\(781\) −5.18497 + 8.98062i −0.185533 + 0.321352i
\(782\) 5.68421 + 9.84535i 0.203267 + 0.352069i
\(783\) 0 0
\(784\) −6.80329 1.64779i −0.242975 0.0588495i
\(785\) 0 0
\(786\) 0 0
\(787\) −27.5015 15.8780i −0.980323 0.565990i −0.0779556 0.996957i \(-0.524839\pi\)
−0.902368 + 0.430967i